Maximum-Likelihood Estimation of Noncompensatory IRT Models With the MH-RM Algorithm

In compensatory'' multidimensional item response theory (IRT) models, latent ability scores are typically assumed to be independent and combine additively to influence the probability of responding to an item correctly. However, testing situations arise where modeling an additive relationship between latent abilities is not appropriate or desired. In these situations, noncompensatory'' models may be better suited to handle this phenomenon. Unfortunately, relatively few estimation studies have been conducted using these types of models and effective estimation of the parameters by maximum-likelihood has not been well established. In this article, the authors demonstrate how noncompensatory models may be estimated with a Metropolis-Hastings Robbins-Monro hybrid (MH-RM) algorithm and perform a computer simulation study to determine how effective this algorithm is at recovering population parameters. Results suggest that although the parameters are not recovered accurately in general, the empirical fit was consistently better than a competing product-constructed IRT model and latent ability scores were also more accurately recovered.